This invention relates generally to positron emission tomography (PET) systems, and more particularly, to the reconstruction of images in a Time-of-Flight PET (TOF-PET) system using an analytical filter.
Positrons are positively charged electrons that are emitted by radionuclide substances. These radionuclide substances, called “radiopharmaceuticals”, are employed as radioactive tracers and are injected in a patient to be scanned. The radionuclide substances decay and emit positrons. The positrons collide with electrons in the patient's body and are annihilated. The annihilation process produces two gamma rays. These gamma rays are referred to as photons. The emitted photons are directed in nearly opposite directions, each with energy of 511 KeV. A PET scanner generates an image by determining the number of such annihilations at each location within a field of view.
A PET scanner typically includes a detector ring assembly. This detector ring assembly includes rings of detectors that encircle the patient. Coincidence detection circuits connect to the detectors and record the detected photons. However, only those photons that are detected within a pre-determined time-interval, called the coincidence window, are recorded. These recorded simultaneous detections are termed coincidence events and the detected photons are termed as coincidence photons. The photons are detected by detectors located on opposite sides of a line joining the detectors and passing through the point of annihilation. The virtual line joining the two detectors that detect a pair of annihilation photons is called a Line Of Response (LOR). Each LOR is characterized by a radial distance (r) from the center of the detector ring, and an angle (θ) from the horizontal axis through the center of the detector ring. The coincidence events detected by a PET scanner are binned together in possible LORs.
The LORs are grouped together into a plurality of sinograms or projection planes, which is the ordering of the LORs on the basis of the radial distance, r, and the angle, θ. The sinograms or projection planes are then transformed by using mathematical operations to generate final output images. This transformation process is called tomographic image reconstruction. The reconstructed image represents the distribution of the activity within the object being scanned.
In the conventional PET systems, according to the tomographic image reconstruction process, the coincident events, also called the annihilation events, can best be localized only across the length of the LOR with uniform probability. The localization is performed using uniform probability as all the coincidence events originating from the line between a pair of detectors are binned together into the corresponding LOR. This basic tomographic image reconstruction technique is called Back-Projection (BP).
The image obtained through BP operation is, however, blurred and distorted. To overcome this problem, a ramp filter is used. This technique is called Filtered Back-Projection (FBP). This technique helps recover high frequencies and prevents blurring of the image.
In a TOF-PET system, in addition to detecting the coincident events inside the coincidence time window, the difference in the detection times between the two photons is stored. This difference in the detection times is called the ‘Time-of-Flight’. The elements of a sinogram in a TOF-PET system have the co-ordinate of TOF, in addition to the radial distance, r, and the angular co-ordinate, θ. Since both of the detected photons travel at the same speed (the constant speed of light), the exact time of flight is indicative of the position along a LOR. For example, the coincidence events with TOF=0 can be localized to the mid-point between the detector pairs. Further, the coincidence events with TOF=1 ns can be localized to 15 cm from the mid-point between the two detectors in the direction of the detector that detected the first photon in the pair. This ability to localize the annihilation event increases the signal-to-noise ratio in the reconstructed image. In practical TOF-PET systems, the measurement of TOF is not exact and there is some uncertainty in its measurement. The extent of uncertainty in the TOF measurement depends on the timing resolution of the detectors. Typically, the uncertainty in the TOF measurement has a Gaussian distribution that is quantified by the Full Width at Half Maximum (FWHM) of the Gaussian distribution. This uncertainty in the measurement of TOF translates to an uncertainty in the localization of the annihilation events. Since the uncertainty in TOF measurement has a Gaussian distribution, the uncertainty in the localization of the annihilation events also has a Gaussian distribution.
During image reconstruction, the localization of events is implemented by distributing (back-projecting) the events in a TOF LOR along the line between the two detectors with a probability based on the timing resolution of the detectors. This process of back projecting timing uncertainty profiles instead of uniform back-projection is called Confidence-Weighted Back-Projection (CW BP). A mathematical model of the CW BP is given by Donald L. Synder et al., in the paper: “A mathematical model for Positron-Emission tomography systems having Time-of-Flight measurements”, IEEE Transactions on Nuclear Science, Vol. NS-28, No. 3, June 1981. Similar to BP, the conventional techniques used for CW BP produces a blurred and distorted image. In particular, a simple ramp filter, similar to the one used in conventional FBP, over-compensates for high frequencies and may produce over and/or under-shoots.
In conventional CW BP, this over-amplification of the high frequencies results from filtering the reconstructed image with a low-pass filter to reduce power in the higher frequencies. The strength of filtering in these systems, by using the conventional CW BP is chosen based on the desired resolution of the image and not accounting for the time-of-flight.